Vibratory meter with pointed flow tube

ABSTRACT

A first and second vibratory meter (5), and methods of manufacturing the same are provided. The first vibratory meter includes a pickoff (170l), a driver (180), and a flow tube (400) comprising a tube perimeter wall with: a first substantially planar section (406a), a second substantially planar section (406b) coupled to the first substantially planar section to form a first angle θ?1#191 (404), and a first curved section (406c). The second vibratory meter includes a pickoff, a driver, and a flow tube (700) comprising a tube perimeter wall with: a first substantially planar section (706a), a second substantially planar section (706b) coupled to the first substantially planar section to form a first angle θ?1#191 (704), a third substantially planar section (706c), a fourth substantially planar section (706d), and a fifth substantially planar section (706e).

TECHNICAL FIELD

The examples described below relate to vibratory meters and flow tubesfor vibratory meters. More particularly, the examples are directed tovibratory meters including flow tubes with pointed sections.

TECHNICAL FIELD

Vibratory meters, such as Coriolis mass flowmeters and vibratingdensitometers, typically operate by detecting motion of a vibrating flowtube that contains a flowing material. Properties associated with thematerial in the flow tube, such as mass flow, density and the like, canbe determined by processing measurement signals received from motiontransducers associated with the flow tube. Vibratory meters have meterassemblies with one or more flow tubes of a straight or curvedconfiguration. Each flow tube configuration in a Coriolis mass flowmeter has a set of natural vibration modes, which may be of simplebending, torsional, or coupled type. Each flow tube can be driven tooscillate at a preferred mode.

As material begins to flow through the flow tube(s), Coriolis forcescause each point along the flow tube(s) to have a different phase. Forexample, the phase at the inlet end of the flowmeter lags the phase atthe centralized driver position, while the phase at the outlet leads thephase at the centralized driver position. Pickoffs on the flow tube(s)produce sinusoidal signals representative of the motion of the flowtube(s). Signals output from the pickoffs are processed to determine thetime delay between the pickoffs. The time delay between the two or morepickoffs is proportional to the mass flow rate of material flowingthrough the flow tube(s).

A meter electronics connected to the driver generates a drive signal tooperate the driver, and to determine a mass flow rate and/or otherproperties of a process material from signals received from thepickoffs. The driver may comprise one of many well-known arrangements;however, a magnet and an opposing drive coil have received great successin the flowmeter industry. An alternating current is passed to the drivecoil for vibrating the flow tube(s) at a desired flow tube amplitude andfrequency. Typically, the pickoffs include a magnet and coil arrangementvery similar to the driver arrangement.

In some applications, it may be desirable to increase the crosssectional area of a flow tube for a vibratory meter to increase fluidflow. Previously, however, it was not always possible to increase thecross sectional area of a flow tube without increasing the size of themeter. Most prior vibratory meters feature flow tubes with circularperimeter walls. Increasing the diameter of a circular flow tubeperimeter wall means extending the dimensions of the flow tube in alldirections, however, which may cause problems in some applications. Forexample, when a Reynolds number is low, typically due to high viscosityof a fluid in the vibratory meter, there may be flow profile effects, orviscosity-related effects, which can reduce the sensitivity of avibratory meter. Typically, a vibratory meter with a tube length l todrive-direction inner tube diameter d (l/d) ratio of 25 or less willexperience flow profile effects. Increasing the diameter d of a flowtube therefore may result in a need to increase the length l of the flowtube, and the size of the meter.

Some newer vibratory meters include multichannel flow tubes.Multichannel flow tubes include one or more channel divisions inside ofthe flow tube perimeter wall that divide the flow tube into two or morechannels. The multichannel flow tubes feature a narrower effectivediameter d_(eff), which can be helpful in preventing flow profileeffects. Multichannel flow tubes can also help prevent decoupling inmultiphase fluids, and velocity of sound (VOS) effects in gases andmultiphase fluids, both of which are sources of errors in meters.

When channel divisions are incorporated into prior vibratory meterdesigns, however, for example in multichannel flow tubes with circulardiameters, the channels reduce the cross-sectional area for flow througha flow tube. This may cause a constriction in the multichannel flowtube.

One way to manufacture flow tubes, either single channel flow tubes ormultichannel flow tubes with their one or more inner channels, is viaadditive manufacturing, or 3D printing. 3D printing is moststraightforward when a part being fabricated includes components thatare perpendicular to the printer bed. When components are orientedparallel to the printer bed, or within a predetermined acute angle ofthe printer bed, however, additional support material may be required toprint the component. It is then necessary to remove the support materialafter the printing is complete.

Prior flow tubes include perimeter tube walls which include sectionsthat are parallel to or nearly parallel to the 3D printer bed. Forexample, a circular perimeter tube wall may require supports to print atthe top and the bottom portions of the perimeter tube wall, relative tothe 3D printer bed.

Accordingly, there is a need for flow tubes and vibratory meters thatcan increase the tube cross sectional area for fluid flow, withoutextending the drive-direction inner diameter d. There is also a need forflow tubes that can be manufactured via additive methods withoutadditional material for support. Such solutions can be realized with apointed flow tube.

SUMMARY

A vibratory meter is provided. The vibratory meter includes a pickoffattached to a flow tube, a driver coupled to the flow tube, the driverbeing configured to vibrate the flow tube, and the flow tube comprisinga tube perimeter wall comprising: a first substantially planar section,a second substantially planar section, coupled to the firstsubstantially planar section to form a first angle θ₁, and a firstcurved section.

A vibratory meter is provided. The vibratory flow meter includes apickoff attached to a flow tube, a driver coupled to the flow tube, thedriver being configured to vibrate the flow tube, and the flow tubecomprising a tube perimeter wall comprising: a first substantiallyplanar section, a second substantially planar section coupled to thefirst substantially planar section to form a first angle θ₁, a thirdsubstantially planar section, a fourth substantially planar section, anda fifth substantially planar section.

A method of forming a vibratory meter is provided. The method includesproviding a flow tube with a tube perimeter wall comprising: a firstsubstantially planar section, a second substantially planar sectioncoupled to the first substantially planar section to form a first angleθ₁, and a first curved section; coupling a driver to the flow tube; andcoupling a pickoff to the flow tube.

A method of forming a vibratory meter is provided. The method comprisesproviding a flow tube with a tube perimeter wall comprising: a firstsubstantially planar section, a second substantially planar sectioncoupled to the first substantially planar section to form a first angleθ₁, a third substantially planar section, a fourth substantially planarsection, and a fifth substantially planar section; coupling a driver tothe flow tube; and coupling a pickoff to the flow tube.

Aspects

In a further aspect, the first angle θ₁ may be less than or equal to 100degrees.

In a further aspect, the first angle θ₁ may be less than or equal to 120degrees.

In a further aspect, the tube perimeter wall further may comprise asecond curved section (506 f) and a third substantially planar section(506 d) coupled to a fourth substantially planar section (506 e),wherein the fifth substantially planar section and the sixthsubstantially planar section form a second angle θ₂ (504).

In a further aspect, the second angle θ₂ may be equal to the first angleθ₁.

In a further aspect, a first pointed section (516 a) to a second pointedsection (516 b) height h (514) may be

${h = \frac{d}{\cos \left( {90 - \frac{\theta \; 1}{2}} \right)}},$

wherein the first pointed section is formed by the first substantiallyplanar section and the second substantially planar section, the secondpointed section is formed by the third substantially planar section andthe fourth substantially planar section, and d is the maximum diameter d(204) of the tube perimeter wall perpendicular to the first pointedsection to second pointed section height h.

In a further aspect, the vibratory meter may further comprise a firstchannel division (606 a) enclosed within and coupled to the tubeperimeter wall, the first channel division and the tube perimeter wallforming a first channel (608 a) and a second channel (608 b) in the flowtube.

In a further aspect, the first channel division may be substantiallyplanar.

In a further aspect, the vibratory meter may further comprise a secondchannel division (606 b) enclosed within and coupled to the tubeperimeter wall, the second channel division dividing the second channeland a third channel (608 c) in the flow tube.

In a further aspect, the second channel division may be substantiallyplanar and substantially parallel to the first channel division.

In a further aspect, the first angle θ₁ may be less than or equal to 100degrees.

In a further aspect, the first angle θ₁ may be less than or equal to 120degrees.

In a further aspect, the vibratory meter may further comprise a sixthsubstantially planar section (806 f), wherein the fifth substantiallyplanar section and the sixth substantially planar section form a secondangle θ₂ (804).

In a further aspect, the second angle θ₂ may be equal to the first angleθ₁.

In a further aspect, a first pointed section (816 a) to a second pointedsection (816 b) height h (514) may be

${h = \frac{d}{\cos \left( {90 - \frac{\theta \; 1}{2}} \right)}},$

wherein the first pointed section is formed by the first substantiallyplanar section and the second substantially planar section, the secondpointed section is formed by the fifth substantially planar section andthe sixth substantially planar section, and d is the maximum diameter d(204) of the tube perimeter wall perpendicular to the first pointedsection to second pointed section height h.

In a further aspect, the vibratory meter may further comprise a firstchannel division (908 a) enclosed within and coupled to the tubeperimeter wall, the first channel division and the tube perimeter wallforming a first channel (910 a) and a second channel (910 b) in the flowtube.

In a further aspect, the first channel division may be substantiallyplanar.

In a further aspect, the vibratory may further comprise a second channeldivision (908 b) enclosed within and coupled to the tube perimeter wall,the second channel division dividing the second channel and a thirdchannel (910 c) in the flow tube.

In a further aspect, the second channel division may be substantiallyplanar and substantially parallel to the first channel division.

In a further aspect, the tube perimeter wall may further comprise asecond curved section; a third substantially planar section; and afourth substantially planar section coupled to the third substantiallyplanar section to form a second angle θ₂, wherein the tube perimeterwall further comprises the second curved section, the third curvedsection, and the fourth substantially planar section.

In a further aspect, a first pointed section (516 a) to a second pointedsection (516 b) height h (514) may be

${h = \frac{d}{\cos \left( {90 - \frac{\theta \; 1}{2}} \right)}},$

wherein the first pointed section is formed by the first substantiallyplanar section and the second substantially planar section, the secondpointed section is formed by the third substantially planar section andthe fourth substantially planar section, and d is the maximum diameter d(204) of the tube perimeter wall perpendicular to the first pointedsection to second pointed section height h.

In a further aspect, the tube perimeter wall may further comprise asixth substantially planar section, wherein the fifth substantiallyplanar section and the sixth substantially planar section form a secondangle θ₂.

In a further aspect, a first pointed section (816 a) to a second pointedsection (816 b) height h (514) may be

${h = \frac{d}{\cos \left( {90 - \frac{\theta \; 1}{2}} \right)}},$

wherein the first pointed section is formed by the first substantiallyplanar section and the second substantially planar section, the secondpointed section is formed by the fifth substantially planar section andthe sixth substantially planar section, and d is the maximum diameter d(204) of the tube perimeter wall perpendicular to the first pointedsection to second pointed section height h.

In a further aspect, the first angle θ₁ may be less than or equal to 100degrees.

In a further aspect, the first angle θ₁ may be less than or equal to 120degrees.

In a further aspect, the first angle θ₁ may be equal to the second angleθ₂.

In a further aspect, the flow tube may further comprise a first channeldivision enclosed within and coupled to the tube perimeter wall, thefirst channel division and the tube perimeter wall forming a firstchannel and a second channel in the flow tube.

In a further aspect, the first channel division may be substantiallyplanar.

In a further aspect, the flow tube may further comprise a second channeldivision enclosed within and coupled to the tube perimeter wall, thesecond channel division dividing the second channel and a third channelin the flow tube.

BRIEF DESCRIPTION OF THE DRAWINGS

The same reference number represents the same element on all drawings.The drawings are not necessarily to scale.

FIG. 1 depicts a vibratory flowmeter, in accordance with an example;

FIG. 2 depicts a cross-section of a flow tube 200;

FIG. 3 depicts a cross-section of a flow tube 300;

FIG. 4 depicts a cross-section of a flow tube 400, in accordance with anexample;

FIG. 5 depicts a cross-section of a flow tube 500, in accordance with anexample;

FIG. 6 depicts a cross-section of a flow tube 600, in accordance with anexample;

FIG. 7 depicts a cross-section of a flow tube 700, in accordance with anexample;

FIG. 8 depicts a cross-section of a flow tube 800, in accordance with anexample;

FIG. 9 depicts a cross-section of a flow tube 900, in accordance with anexample;

FIG. 10 depicts a method 1000, in accordance with an example; and

FIG. 11 depicts a method 1100, in accordance with an example.

DETAILED DESCRIPTION

The present disclosure describes vibratory meters including flow tubeswith a pointed section, and methods of forming a vibratory meterincluding the flow tubes with a pointed section.

FIG. 1 depicts a vibratory meter 5 with a multichannel flow tube 130 inaccordance with an example. As shown in FIG. 1, the vibratory meter 5comprises a meter assembly 10 and meter electronics 20. The meterassembly 10 responds to the mass flow rate and density of a processmaterial. The meter electronics 20 is connected to the meter assembly 10via leads 100 to provide density, mass flow rate, and temperatureinformation over communications path 26, as well as other information.Information and commands may be further received at meter electronics 20over communications path 26.

A Coriolis flow meter structure is described, although this is notintended to be limiting. Those of skill will readily understand that thepresent Application could be practiced as a vibrating tube densitometer,tuning fork densitometer, or the like.

The meter assembly 10 includes a pair of manifolds 150 and 150′, flanges103 and 103′ having flange necks 110 and 110′, a pair of parallel flowtubes 130 and 130′, driver 180, and a pair of pick-off sensors 170 l and170 r. Flow tubes 130 and 130′ have two essentially straight inlet legs131, 131′ and outlet legs 133, 133′, which converge towards each otherat flow tube mounting blocks 120 and 120′. The flow tubes 130, 130′ bendat two symmetrical locations along their length and are essentiallyparallel throughout their length. Brace bars 140 and 140′ serve todefine the axis W and W′ about which each flow tube 130, 130′oscillates. The legs 131, 131′ and 133, 133′ of the flow tubes 130, 130′are fixedly attached to flow tube mounting blocks 120 and 120′ and theseblocks, in turn, are fixedly attached to manifolds 150 and 150′. Thisprovides a continuous closed material path through meter assembly 10.

When flanges 103 and 103′, having holes 102 and 102′ are connected, viainlet end 104 and outlet end 104′ into a process line (not shown) whichcarries the process material that is being measured, material entersinlet end 104 of the meter through an orifice 101 in the flange 103 andis conducted through the manifold 150 to the flow tube mounting block120 having a surface 121. Within the manifold 150, the material isdivided and routed through the flow tubes 130, 130′. Upon exiting theflow tubes 130, 130′, the process material is recombined in a singlestream within the flow tube mounting block 120′ having a surface 121′and the manifold 150′ and is thereafter routed to outlet end 104′connected by the flange 103′ having holes 102′ to the process line (notshown).

The flow tubes 130, 130′ are selected and appropriately mounted to theflow tube mounting blocks 120, 120′ to have substantially the same massdistribution, moments of inertia and Young's modulus about bending axesW--W and W′--W′, respectively. These bending axes go through the bracebars 140, 140′.

Both flow tubes 130, 130′ are driven by driver 180 in oppositedirections about their respective bending axes W and W′ and at what istermed the first out-of-phase bending mode of the flow meter. Thisdriver 180 may comprise any one of many well-known arrangements, such asa magnet mounted to the flow tube 130′ and an opposing coil mounted tothe flow tube 130 and through which an alternating current is passed forvibrating both flow tubes 130, 130′. A suitable drive signal is appliedby the meter electronics 20, via lead 185, to the driver 180.

The meter electronics 20 receives the left and right sensor signalsappearing on leads 1651, 165 r, respectively. The meter electronics 20produces the drive signal appearing on lead 185 to driver 180 andvibrate flow tubes 130, 130′. The meter electronics 20 processes theleft and right sensor signals and the RTD signal to compute the massflow rate and the density of the material passing through meter assembly10. This information, along with other information, may be transmittedby meter electronics 20 over communications path 26.

While FIG. 1 depicts a single meter assembly 10 in communication withmeter electronics 20, those skilled in the art will readily appreciatethat multiple sensor assemblies may be in communication with meterelectronics 20. Further, meter electronics 20 may be capable ofoperating a variety of different sensor types. Each sensor assembly,such as the meter assembly 10 in communication with meter electronics20, may have a dedicated section of a storage system within meterelectronics 20.

Meter electronics 20 may include various other components and functions,as will be understood by those of skill. These additional features maybe omitted from the description and the figures for brevity and clarity.

Vibratory meter 5 includes flow tubes 130, 130′. Flow tubes 130, 130′have a plurality of fluid channels through which a material, such as asingle phase or multiphase fluid, can flow. That is, the fluid flowingthrough the flow tubes 130, 130′ may flow through two or more fluidchannels.

FIGS. 2-9 each represent an example cross section of flow tube 130, 130′that will be discussed below. The example flow tube cross section isrepresented by the line indicated by 2-2 indicated in FIG. 1.

FIG. 2 depicts a cross section of a prior flow tube 200. Flow tube 200includes a tube perimeter wall 202 that is shaped in a circle. FIG. 2indicates the drive direction of the vibratory meter. Sometimes it isdesirable to increase the total cross sectional area of a flow tube toincrease the fluid flow capacity in a meter. Prior solutions includedincreasing the inner diameter d 204 of tube perimeter wall 202. However,flow profile effects increase when the ratio of the flow tube length lto its inner diameter d in the drive direction is relatively low.Therefore, for some applications, increasing the radius of circular flowtube 200 without also increasing the flow tube length l, and the size ofvibratory meter, is not possible without losing meter accuracy.

FIG. 3 represents a further cross section of a prior multichannel flowtube 300. Flow tube 300 is like flow tube 200 in that it also includes atube perimeter wall 202, but it differs in that it includes one or morechannel divisions 306 a-306 c. One or more channel divisions 306 a-306 care configured to provide two or more channels 308 a-308 d. Each channel308 a-308 d features a reduced effective diameter d_(eff) in at leastone direction, which, in the example of flow tube 300, is the drivedirection of the vibratory meter. The narrower effective diameterd_(eff) 304 may allow for a reduction in decoupling of multiphasefluids, a reduction in velocity of sound errors, and a reduction in flowprofile effects.

The additional channel divisions 306 a-306 c provided with flow tube 300may reduce the total cross sectional area through which a fluid maypass, however. Therefore, flow tube 300 may be more constricted thanflow tube 200.

FIG. 4 depicts a cross section of flow tube 400 in accordance with anexample. Flow tube 400 includes a tube perimeter wall 402. A tubeperimeter wall surrounds and contains fluid in a flow tube.

Tube perimeter wall 402 includes a first substantially planar section, asecond substantially planar section, coupled to the first substantiallyplanar section to form a first angle θ₁, and a first curved section. Forexample, tube perimeter wall 402 includes first substantially planarsection 406 a, second substantially planar section 406 b, and firstcurved section 406 c. In the example, first and second substantiallyplanar sections 406 a, 406 b, and first curved section 406 c combine toform a teardrop cross sectional shape, with first and secondsubstantially planar sections 406 a, 406 b forming a pointed sectionthat points outward from the tube perimeter wall 402, as defined byfirst angle θ₁ 404.

By substantially planar, first and second substantially planar sections406 a, 406 b may each include a cross sectional area that is primarilycontained in a rectangular area with a width that is a small proportionof the length. While FIG. 4 depicts the first and second substantiallyplanar sections 406 a and 406 b as being strictly planar, this is notintended to be limiting. In examples, a substantially planar section mayinclude a few uneven, or non-planar portions.

Tube perimeter wall 402 further includes a first curved section 406 c. Acurved section may take a circular, oval, elliptical, or any other kindof rounded shape. In the example of flow tube 400, first curved section406 c is primarily circular.

First and second substantially planar sections 406 a and 406 b arecoupled together to form a first angle θ₁. First angle θ₁ 404 ismeasured from the interior of tube perimeter wall 402, as may be seen inFIG. 4.

By providing a curved section 406 c, which may in examples be sized tohave the same diameter d 204 as prior art flow tubes such as flow tubes200 and 300, flow tube 400 may be retrofitted into the same vibratorymeters as flow tubes 200 and 300 with minimal design changes. This issuggested by the dotted line in FIG. 4, which represents the innerdiameter of flow tube 200. Because diameter d 204 does not increase overflow tubes 200 and 300, however, flow tube 400 will not increase theflow profile effects of a meter into which it is retrofitted.

Flow tube 400 features an additional pointed section defined by firstand second substantially planar sections 406 a and 406 b, which mayallow flow tube 400 to increase the cross sectional area over whichfluid may flow, without a need to increase the overall size of thevibratory meter.

In examples, flow tube 400 may offer the most additional cross sectionalarea when first angle θ₁ is smaller, because this may allow the pointedsection of flow tube 400 to extend the furthest in a directionperpendicular to the diameter d 204. In examples, the first angle θ₁ maybe no larger than 100 degrees. In further examples, the first angle θ₁may be less than or equal to 120 degrees, however. In further examples,any angle may be possible to control the flow of fluid through flow tube400, as will be understood by those of skill.

FIG. 5 depicts a cross section of flow tube 500 in accordance with afurther example. Flow tube 500 is similar to flow tube 400, except thatit further includes a second curved section 506 f and a thirdsubstantially planar section 506 d coupled to a fourth substantiallyplanar section 506 e.

Flow tube 500 has a tube perimeter wall 502 with profile that includestwo pointed sections and a rounded center. This may allow flow tube 500to be easily retrofitted into the same vibratory meters as flow tubes200 or 300, but with two pointed sections to further expand thecross-sectional area of the tube perimeter wall 502 and allow additionalfluid flow in a vibratory meter.

The third substantially planar section 506 d and the fourthsubstantially planar section 506 e form a second angle θ₂ 504. Inexamples, the first angle θ₁ 404 may be equal to the second angle θ₂.This may provide symmetry about an axis transverse to flow in flow tube500. This may help balance the mass of the components of a vibratorymeter, thereby allowing for easier retrofitting into vibratory meterswith prior symmetrical circular flow tubes.

In further examples, however, first angle θ₁ may not be equal to thesecond angle η₂.

In examples where the first angle θ₁ and the second angle θ₂ are thesame, a first pointed section 516 a to a second pointed section 516 bheight h 514, as depicted in FIG. 5, may be equal to:

$\begin{matrix}{{h = \frac{d}{\cos \left( {90 - \frac{\theta \; 1}{2}} \right)}},} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

where the first pointed section 516 a is formed by the firstsubstantially planar section 506 a and the second substantially planarsection 506 b, the second pointed section 516 b is formed by the thirdsubstantially planar section 506 d and the fourth substantially planarsection 506 e, and d is the maximum diameter of the tube perimeter wallin a plane perpendicular to the first pointed section to second pointedsection height h. In examples, maximum diameter d may be an inner tubediameter, an outer tube diameter, or a center tube diameter. Forexample, maximum diameter d may be maximum diameter d 204, as depictedin FIG. 4 or 5.

In examples, flow tube perimeter walls 402 or 502 may be formed over amandrel and seam welded, via an extrusion process, via a subtractivemanufacturing process, for example using machining, electrical dischargemachining, electrochemical machining, electron beam machining,photochemical machining, or ultrasonic machining, or via an additivemanufacturing or three-dimensional (3D) printing techniques, for exampleusing stereolithography, digital light processing, fused depositionmodeling, selective laser sintering, selective laser melting, electronicbeam melting, or laminated object manufacturing.

In instances where it is desirable to fabricate a flow tube via 3Dprinting, flow tubes 400 and 500 may offer further advantages over flowtubes 200 and 300. In some applications, it can be challenging to use 3Dprinting to fabricate sections of parts that are oriented within aminimum angle of parallel to the printer bed. This may be seen in FIG.5, which depicts printer bed plane 510 and minimum print angle θ_(min)512. If a section of a part is oriented to be below minimum print angleθ_(min) 512, additional material will need to be printed under thatsection as a support to fabricate the part. In some applications,minimum angle θ_(min) 512 may be 45 degrees for 3D printingapplications. In further applications, however, minimum angle θ_(min)512 may be 40 degrees, 30 degrees, 20 degrees, or even less.

Prior flow tubes 200 and 300 are circular, and include sections that areparallel to or nearly parallel to the 3D printer bed. A circularperimeter tube wall, for example, may require supports below the bottomof the flow tube perimeter wall, outside of the flow tube, and/or at thetop of the flow tube perimeter wall, inside the flow tube. Supportmaterial that is printed inside the tube perimeter wall may requireremoval after printing, however, which can be difficult, and sometimeseven impossible to do.

The pointed section of first and second substantially planar sections406 a and 406 b may be printed so that it is pointing directly towardsor away from printer bed 510. If minimum print angle θ_(min) 512 is 50degrees, then a first angle θ₁ that is 100 degrees or less will make itfeasible to print flow tube 500 without additional support materialexternal to flow tube 500. In the case that first and secondsubstantially planar sections 406 a and 406 b may be printed so thatthey are pointing directly towards printer bed 510, as depicted in FIG.5, this may prevent a need for support material external to flow tube500. In the case that first and second substantially planar sections 406a and 406 b may be printed so that they point away from printer bed 510,however (not pictured) this may prevent a need for support materialinternal to flow tube 500. Self-supported flow tube 500 may provide forless wasted material during manufacturing, in addition to eliminatingthe need for the extra step of removing the support material afterprinting flow tube 500.

FIG. 6 depicts a cross section of multichannel flow tube 600 inaccordance with a further example. Flow tube 600 is similar to flow tube500, except that it further includes a first channel division enclosedwithin and coupled to the tube perimeter wall, the first channeldivision and the tube perimeter wall forming a first channel and asecond channel in the flow tube. Channel divisions may be coupled to aflow tube perimeter wall in one or two sections, with respect to tubeperimeter wall 402 or 502, to divide a single flow tube into two or morechannels. For example, channel division 606 a divides flow tube 600 intochannels 608 a and 608 b.

Channel divisions may be coupled to a flow tube perimeter wall along alongitudinal section of the flow tube. In examples, the channeldivisions may be coupled to the flow tube perimeter wall along theentire longitudinal extent of the flow tube, along the vibratory sectionof the flow tube, along a portion of the vibratory section of the flowtube, or along any other longitudinal section of the flow tube.

In examples, the first channel division may be substantially planar. Infurther embodiments, however, the one or more channel divisions 606a-606 d may include a curvilinear cross section, a substantiallycircular cross section, or any other cross section known to those ofskill.

For example, flow tube 600 depicts substantially planar channeldivisions 606 a-606 d. In the example of flow tube 600, thesubstantially planar channel divisions 606 a-606 d are perpendicular tothe drive direction. In examples, however, channel divisions 606 a-606 dmay not be oriented to be perpendicular to the drive direction. Infurther examples, however, the orientation of channel divisions 606a-606 d may change from cross sectional area to cross sectional area ofvibratory meter 10.

In examples, flow tube 600 may further comprise a second channeldivision enclosed within and coupled to the tube perimeter wall, thesecond channel division dividing the second channel and a third channelin the flow tube. For example, channel divisions 606 a-606 d divide flowtube 600 into channels 608 a-608 e. In examples, any number of channeldivisions are possible, as will be understood by those of skill.

In examples, the second channel division 606 b may be substantiallyplanar, and/or substantially parallel to the first channel division 606a.

Flow tube 600 may allow for a multichannel flow tube to have a crosssectional area with expanded space for fluid flow in the additional oneor more pointed regions over prior flow tubes. This may allow flow tube600 to compensate for the cross-sectional area lost due to the thicknessof the one or more channel divisions 606 a-606 d.

While flow tube 600 is depicted as including two pointed regions, thoseof skill will readily understand that one or more channel divisions mayalso be included with flow tube 400 to provide additional crosssectional area for a multichannel flow tube.

FIG. 7 depicts a cross section of further flow tube 700 in accordancewith an example. Flow tube 700 includes a tube perimeter wall with afirst substantially planar section, a second substantially planarsection coupled to the first substantially planar section to form afirst angle θ₁, a third substantially planar section, a fourthsubstantially planar section, and a fifth substantially planar section.For example, flow tube perimeter 702 includes first, second, third,fourth, and fifth substantially planar sections 706 a, 706 b, 706 c, 706d, and 706 e, respectively. The cross section of flow tube 700 forms apentagonal shape, with first and second substantially planar sections706 a and 706 b forming a pointed section with a first angle θ₁ 704.

Flow tube 700 may provide the same advantages described with regards toflow tubes 400, 500, and 600. In particular, flow tube 700 may allow foran expanded area for fluid to flow through a flow tube, for singlechannel or multichannel flow tubes.

In examples, the first angle θ₁ 704 may be less than or equal to 100degrees. In further examples, the first angle θ₁ 704 may be less than orequal to 120 degrees. This may maximize for additional cross sectionalarea in flow tube 700. In addition, the pointed section of flow tube mayprovide for self-supported flow tube design for 3D printing.

FIG. 8 depicts a cross section of flow tube 800 in accordance with afurther example. Flow tube 800 is like flow tube 700, with theadditional feature that tube perimeter wall 802 includes a sixthsubstantially planar section. The fifth substantially planar section 806e and the sixth substantially planar section 806 f form a second angleθ₂ 804. Flow tube perimeter wall 802 of flow tube 800 takes the form ofa hexagon, with first and second substantially planar sections 706 a and706 b forming a first pointed section defined by first angle θ₁ 704, andfifth substantially planar section 806 e and the sixth substantiallyplanar section 806 f defined by a second angle θ₂ 804.

Flow tube 800 may allow for additional cross sectional area over flowtube 700, without increasing the overall size of the vibratory meter.

In examples, the second angle θ₂ 804 may be equal to the first angle θ₁704. This may provide for a symmetrical flow tube cross section in adirection transverse to the flow direction.

In examples, a first pointed section 816 a to a second pointed section816 b height

${{h\; 514\mspace{14mu} {is}\mspace{20mu} h} = \frac{d}{\cos \left( {90 - \frac{\theta \; 1}{2}} \right)}},$

where the first pointed section 816 a is formed by the firstsubstantially planar section 706 a and the second substantially planarsection 706 b, the second pointed section 816 b is formed by the fifthsubstantially planar section 806 e and the sixth substantially planarsection 806 f, and d is the maximum diameter d of the tube perimeterwall perpendicular to the first pointed section to second pointedsection height h, as described with regards to Equation 1 above.

FIG. 9 depicts a cross section of flow tube 900 in accordance with afurther example. Flow tube 900 is a multichannel version of flow tube800. Flow tube 900 includes a first channel division 908 a enclosedwithin and coupled to the tube perimeter wall 802, the first channeldivision 908 a and the tube perimeter wall 802 forming a first channel910 a and a second channel 910 b in the flow tube.

In examples, the first channel division may be substantially planar.

In examples, a second channel division 908 b may be enclosed within andcoupled to the tube perimeter wall 802, the second channel division 908b dividing the second channel 910 b and a third channel 910 c in theflow tube.

In examples, the second channel division may be substantially planar andsubstantially parallel to the first channel division.

In examples, the pointed sections of flow tubes 400, 500, 600, 700, 800,and 900 defined by first and second angles θ₁ and θ₂, 404, 504 a, 504 b,704, and 804 may be included along the entire longitudinal length offlow tubes 130, 130′. In further examples, however, first and secondangles θ₁ and θ₂, 404, 504 a, 504 b, 704, and 804 may be included alongonly a portion of the longitudinal length of flow tubes 130, 130′. Otherportions may be circular, for example, or any other cross section knownto those of skill.

FIG. 10 depicts a method 1000, in accordance with an example. Method1000 begins with step 1002. In step 1002, a flow tube with a tubeperimeter wall is provided. The tube perimeter wall comprises a firstsubstantially planar section, a second substantially planar sectioncoupled to the first substantially planar section to form a first angleθ₁, and a first curved section. For example, tube perimeter wall 402,502 includes first substantially planar section 406 a, 506 a and secondsubstantially planar section 406 b, 506 b, which are coupled to formfirst angle θ₁ 404, 504 a, and first curved section 406 c, 506 c.

Method 1000 continues with step 1004. In step 1004, a driver is coupledto the flow tube. For example, driver 180 may be coupled to flow tube130, 130′, 400, 500, 600, 800, or 900. In examples, driver 180 may becoupled to the flow tube using a mounting bracket that is welded,brazed, glued, or fastened to the flow tube. In further examples, amounting bracket, or a portion of the driver, may be integrated into theflow tube. In further examples, driver 180 may be coupled to the flowtube using any technique known to those of skill.

Method 1000 continues with step 1006. In step 1006, a pickoff is coupledto the flow tube. For example, pickoff 170 l, 170 r may be coupled toflow tube 130, 130′, 400, 500, 600, 800, or 900. Like step 1004, pickoff170 l, 170 r may be coupled to the flow tube using a mounting bracketthat is welded, brazed, glued, or fastened to the flow tube. In furtherexamples, a mounting bracket, or a portion of the pickoff 170 l, 170 r,may be integrated into the flow tube. In further examples, pickoff 170l, 170 r may be coupled to the flow tube using any technique known tothose of skill.

In examples of method 1000, the flow tube perimeter may further includea second curved section, a third substantially planar section, and afourth substantially planar section coupled to the third substantiallyplanar section to form a second angle θ₂, wherein the tube perimeterwall further comprises the second curved section, the third curvedsection, and the fourth substantially planar section. For example, tubeperimeter wall 502 of flow tube 500 may include second curved section506 f, and third and fourth substantially planar sections 506 d, 506 e,which define second angle θ₂ 504 b.

FIG. 11 depicts a method 1100, in accordance with an example. Method1100 begins with step 1102. In step 1102, a flow tube with a tubeperimeter wall is provided comprising a first substantially planarsection, a second substantially planar section coupled to the firstsubstantially planar section to form a first angle θ₁, a thirdsubstantially planar section, a fourth substantially planar section, anda fifth substantially planar section. For example, flow tube 700 maycomprise tube perimeter wall 702, including first and secondsubstantially planar sections 706 a, 706 b, which form a first angle θ₁704, and third, fourth, and fifth substantially planar sections 706 c,706 d, and 706 e.

Method 1100 continues with steps 1104 and 1106. Steps 1104 and 1106 aresimilar to steps 1004 and 1006. In step 1104, a driver is coupled to theflow tube. In step 1106, a pickoff is coupled to the flow tube.

In examples of method 1100, the tube perimeter wall may further comprisea sixth substantially planar section, wherein the fifth substantiallyplanar section and the sixth substantially planar section form a secondangle θ₂. For example, flow tubes 800 and 900 may include sixthsubstantially planar section 806 f to form second angle θ₂ 804.

Methods 1000 and 1100 may allow for the manufacturing of a flow tubethat provides an expanded cross sectional area under one or more pointedsections defined by first angle θ₁ or second angle θ₂. This may providefor the manufacturing of a flow tube with additional flow.

In examples of methods 1000 or 1100, the first angle θ₁ may be less thanor equal to 100 degrees. In further examples of methods 1000 or 1100,the first angle θ₁ may be less than or equal to 120 degrees. This mayallow for the manufacturing of a flow tube that can be 3D printedwithout additional material supports.

In examples of methods 1000 or 1100, the first angle θ₁ may be equal tothe second angle θ₂. This may allow for the manufacturing of a flow tubewith symmetry in the direction transverse to the fluid flow.

In examples of methods 1000 or 1100, a first pointed section 816 a tosecond pointed section 816 b height h may be

${h = \frac{d}{\cos \left( {90 - \frac{\theta \; 1}{2}} \right)}},$

where the first pointed section 816 a is formed by the firstsubstantially planar section 706 a and the second substantially planarsection 706 b, the second pointed section 816 b is formed by the fifthsubstantially planar section 806 e and the sixth substantially planarsection 806 f, and d is the maximum diameter d (204) of the tubeperimeter wall perpendicular to the first pointed section to secondpointed section height h, as described with regards to Equation 1 above.

In examples of methods 1000 or 1100, a first channel division may beenclosed within and coupled to the tube perimeter wall, the firstchannel division and the tube perimeter wall forming a first channel anda second channel in the flow tube.

In examples of methods 1000 or 1100, the first channel division may besubstantially planar.

In examples of methods 1000 or 1100, a second channel division may beenclosed within and coupled to the tube perimeter wall, the secondchannel division dividing the second channel and a third channel in theflow tube.

Providing for the manufacture of a multichannel flow tube withadditional cross sectional area may allow for the accommodation of thecross sectional area lost from the channel division wall width.

The devices and methods disclosed herein may help preserve meteraccuracy while increasing the cross-sectional area of a flow tube.Accordingly, flow tubes 300, 400, 500, 600, 700, 800, and 900 may beretrofitted into existing vibratory meter designs, to realize thebenefits associated with the larger cross sectional area diameter. Inaddition, flow tubes 300, 400, 500, 600, 700, 800, and 900 may be moreeasily fabricated via additive manufacturing without a need to provideadditional support material.

The detailed descriptions of the above examples are not exhaustivedescriptions of all examples contemplated by the inventors to be withinthe scope of the Application. Indeed, persons skilled in the art willrecognize that certain elements of the above-described examples mayvariously be combined or eliminated to create further examples, and suchfurther examples fall within the scope and teachings of the Application.It will also be apparent to those of ordinary skill in the art that theabove-described examples may be combined in whole or in part to createadditional examples within the scope and teachings of the Application.Accordingly, the scope of the Application should be determined from thefollowing claims.

1. A vibratory meter (5) comprising: a pickoff (170 l, 170 r) attachedto a flow tube (400, 500, 600, 700, 800, 900); a driver (180) coupled tothe flow tube, the driver being configured to vibrate the flow tube; andthe flow tube comprising a tube perimeter wall (402, 502, 702, 802)comprising: a first substantially planar section (406 a, 506 a), asecond substantially planar section (406 b, 506 b), coupled to the firstsubstantially planar section to form a first angle θ₁ (404), and a firstcurved section (406 c, 506 c).
 2. A vibratory meter as claimed in claim1, wherein the first angle θ₁ is less than or equal to 100 degrees.
 3. Avibratory meter as claimed in claim 1, wherein the first angle θ₁ isless than or equal to 120 degrees.
 4. A vibratory meter as claimed inclaim 1, wherein the tube perimeter wall further comprises a secondcurved section (506 f) and a third substantially planar section (506 d)coupled to a fourth substantially planar section (506 e), wherein thefifth substantially planar section and the sixth substantially planarsection form a second angle θ₂ (504).
 5. A vibratory meter as claimed inclaim 1, wherein the second angle θ₂ is equal to the first angle θ₁. 6.A vibratory meter as claimed in claim 5, wherein a first pointed section(516 a) to a second pointed section (516 b) height h (514) is${h = \frac{d}{\cos \left( {90 - \frac{\theta \; 1}{2}} \right)}},$wherein the first pointed section is formed by the first substantiallyplanar section and the second substantially planar section, the secondpointed section is formed by the third substantially planar section andthe fourth substantially planar section, and d is the maximum diameter d(204) of the tube perimeter wall perpendicular to the first pointedsection to second pointed section height h.
 7. A vibratory meter asclaimed in claim 1, further comprising: a first channel division (606 a)enclosed within and coupled to the tube perimeter wall, the firstchannel division and the tube perimeter wall forming a first channel(608 a) and a second channel (608 b) in the flow tube.
 8. A vibratorymeter as claimed in claim 7, wherein the first channel division issubstantially planar.
 9. A vibratory meter as claimed in claim 7,further comprising: a second channel division (606 b) enclosed withinand coupled to the tube perimeter wall, the second channel divisiondividing the second channel and a third channel (608 c) in the flowtube.
 10. A vibratory meter as claimed in claim 9, wherein the secondchannel division is substantially planar and substantially parallel tothe first channel division. 11-20. (canceled)
 21. A method of forming avibratory meter, the method comprising: providing a flow tube with atube perimeter wall comprising: a first substantially planar section, asecond substantially planar section coupled to the first substantiallyplanar section to form a first angle θ₁, and a first curved section;coupling a driver to the flow tube; and coupling a pickoff to the flowtube.
 22. A method of forming a vibratory meter as claimed in claim 21,wherein the tube perimeter wall further comprises: a second curvedsection; a third substantially planar section; and a fourthsubstantially planar section coupled to the third substantially planarsection to form a second angle θ₂, wherein the tube perimeter wallfurther comprises the second curved section, the third curved section,and the fourth substantially planar section.
 23. A method of forming avibratory meter as claimed in claim 22, wherein a first pointed section(516 a) to a second pointed section (516 b) height h (514) is${h = \frac{d}{\cos \left( {90 - \frac{\theta \; 1}{2}} \right)}},$wherein the first pointed section is formed by the first substantiallyplanar section and the second substantially planar section, the secondpointed section is formed by the third substantially planar section andthe fourth substantially planar section, and d is the maximum diameter d(204) of the tube perimeter wall perpendicular to the first pointedsection to second pointed section height h. 24-26. (canceled)
 27. Amethod as claimed in claim 21, wherein the first angle θ₁ is less thanor equal to 100 degrees.
 28. A method as claimed in claim 21, whereinthe first angle θ₁ is less than or equal to 120 degrees.
 29. A method asclaimed in claim 22, wherein the first angle θ₁ is equal to the secondangle θ₂.
 30. A method as claimed in claim 21, wherein the flow tubefurther comprises a first channel division enclosed within and coupledto the tube perimeter wall, the first channel division and the tubeperimeter wall forming a first channel and a second channel in the flowtube.
 31. A method as claimed in claim 21, wherein the first channeldivision is substantially planar.
 32. A vibratory meter as claimed inclaim 21, wherein the flow tube further comprises a second channeldivision enclosed within and coupled to the tube perimeter wall, thesecond channel division dividing the second channel and a third channelin the flow tube.